C₂₃×#1913 #15669532

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1913
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#1913

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#386
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂₃×#534	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂⁴×C₂₃ ◁ G

380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,29,33,37)(27,34,35,30)(28,31)(32,36)(38,39);(24,26)(25,29,31,37)(27,32)(28,33)(30,36,34,39)(35,38);(24,27)(25,30)(26,32)(28,35)(29,36)(31,34)(33,38)(37,39)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12753, C₂₃×#12754, C₂₃×#12767, …
maximal normal subgroup of	C₂₃×#12753, C₂₃×#12754, C₂₃×#12767, …
maximal quotient of	C₂₃×#9107, C₂₃×#9108, C₂₃×#9109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 645);